where \(\mathbb {E}_t[\,\cdot \,]=\mathbb {E}[\,\cdot \,|\,{\cal F}_t]\)  ([1]}). It is known ([2]}, [3]}) that the above is a convex risk measure (not coherent), on the set
\({E}_\gamma ^1=\Big \lbrace \xi \in L^1_{{\cal F}_T}(\Omega ;\mathbb {R})\bigm |\sup _{t\in [0,T]}\mathbb {E}_t\big [e^{-\gamma \xi }\big ]<\infty \Big \rbrace .\) 
